The man on the screen looks and sounds like Peter Cook and tells the Cook jokes: 'I could have been a judge but I never had the Latin.' But it is a bit like a dead person you meet in a dream. You know who they are but they don't look quite right and are tantalisingly and disappointingly unlike the real person you remember when you wake up.

I had this kind of experience watching Rhys Ifans impersonating my long-time friend and collaborator Peter Cook in Channel 4's Not Only But Always, a 'biopic' written and directed by Terry Johnson which chronicles the ups and downs, but mainly downs, of Peter's life and especially his long collaboration with Dudley Moore, the other half of the famous Pete and Dud duo.

Already, friends and relatives who have seen a preview are complaining about all the errors of fact which seem to be a hallmark of this kind of film. Something that happened in Australia is for some reason transferred to America. Cook's public school, Radley, looks remarkably like Harrow. And so on. Not that any of it matters very much. What does matter is the distorted picture the film gives of Peter Cook.

The Sixties had a way of conferring overnight fame on people when they were very young. I remember in particular how my schoolboy friend Willie Rushton became a celebrity aged 25 when he appeared with David Frost on That Was The Week That Was. Jonathan Miller compared himself and his fellow-performers (Cook, Moore and Alan Bennett) in Beyond the Fringe to the Beatles. Good-looking and supremely self-confident, Cook was the Paul McCartney, the natural leader. It is hard for those who remember him only in later years, a rather shambling, overweight figure traipsing round Soho or Hampstead, to realise just how smart, chic and fashionable he was in his Sixties heyday.

The difficulty facing anyone like Johnson trying to recreate Cook is that that side of him, which is what his best friends remember, can never be recaptured. It is a sad fact that when people are really enjoying themselves and laughing immoderately, they can afterwards remember very little of the conversation, very few of the jokes.

There was the famous occasion when Peter addressed a group of revellers at a lunch celebrating 25 years of Private Eye. Almost everyone who was there, myself included, will tell you it was the funniest, most brilliant speech they had ever heard. But ask us to recall the jokes and there will be a complete blank.

Peter's funniest performances were generally of this impromptu, unscripted variety. I remember in the early days of the Eye how he used to come into the office and make hoax telephone calls. Once, when he had seen a group of native African dancers performing topless on the BBC, he rang an official at the corporation claiming to be Sidney Darlow, the manager of Sidney Darlow dancers, wanting to know why his troupe of white women could not dance naked on television just like the black ones had done. On another occasion, he spoke to quite a senior official at the Foreign Office, telling him at great and manic length how the Russians were spying on him down his drainpipes.

Dudley Moore played no part in the Private Eye pranks except when we recorded the flexi-discs that we used to stick on the Christmas issue. Once we did a send-up of the King's College, Cambridge, carol service, at the end of which Dudley sang in falsetto 'How beautiful are the feet' while Peter improvised in the foreground. 'Oh, they're lovely feet.'

Dudley also played the part of Spiggy Topes, leader of the Turds, 'a popular singing group' (one of Peter's inventions). 'Spiggy,' said Peter in the person of Irish TV chatshow host Eamon Andrews. 'I believe you and your group were once turned out of a London hotel.' 'Yeah, that's quite correct Eamon,' Spiggy replied, 'we went in there perfectly normally dressed wearing gold lamé knickers and feathers up our bottoms.' 'And yet they turned you away,' Peter added in a throwaway, almost certainly improvised, that somehow made the interview instantly memorable.

After those recording sessions, I only saw Dudley Moore once again, before I saw him for the last time at Peter's memorial service in Hampstead. We were both guests of the Radio 4 programme Start the Week. I was looking forward to seeing him again but he hardly seemed to recognise me. It was as if the jokey person I had once fooled around with in the recording studio had somehow been obliterated. Rightly or wrongly, I put this down to the fact that he had become heavily involved with American therapists and in the process of trying to master imaginary phobias and neuroses had managed to lose his personality altogether.

In Johnson's film, the central tragic figure is Peter Cook when it might have made more sense to focus on Moore. Their relationship was a bit like that of Spike Milligan and Peter Sellers, also the subject of a recent 'biopic'. Milligan was generally considered the mad one but compared with those of Sellers his lunacies were trivial. Milligan never lost his strong sense of the absurdities of human existence, but Sellers, caught up in the Hollywood fantasy world, became increasingly and unpleasantly balanced. Moore, with a similar string of unhappy relationships with women, suffered the same sort of fate.

Cook could never be described as mad. But the Cook that Rhys Ifans gives us is a thoroughly unsympathetic character, horrid to Dudley, cruel to his wives. There is none of his charm, none of his basic sweetness of character. It is undeniable that he had another side to him. But that had a very simple explanation, namely that he was an alcoholic and it is well known that alcoholics tend to take it out on those nearest to them, their wives and close colleagues.

So it is hardly surprising that Dudley and his three wives had to put up with some appalling behaviour. All I can say is that over the many years I knew Peter, he was never cruel to me. I was interested to hear that Joe McGrath, the brilliant producer of Not Only But Also (the Cook / Moore masterpiece, most of which the BBC managed to destroy), said the same thing. Unlike Barry Humphries, another comic genius who took to drink in a big way in the Sixties, Peter was never able to conquer his addiction. And it eventually ruined him as a performer, because it ruined that sense of timing which is essential to any comic. I never saw Peter completely plastered but like Dr Johnson's school-friend, the Rev Charles Congreve, he was always 'muddy' (and, like Congreve, he liked to be left alone so that he could drink in private). Humphries became a lifelong member of AA. But perhaps because AA works on religious principles, Peter could never go along with it. With the help of his psychiatrist, the remarkable Dr Max Glatt, he did attend a number of meetings and even set up his own 'secular' group but he was never able to stick with it. In one of his short periods of sobriety towards the end, he recorded a brilliant programme of spoof interviews with Clive Anderson, which gave younger viewers, unfamiliar with the Cook of the Sixties, a glimpse of the old magic. Shortly afterwards, following the death of his mother, he was back on the bottle.

It seems to be the fate of comedians to be remembered now not for their jokes and their genius - even though these are preserved on film - but for their personal fads and failings. This misplaced emphasis tends to confirm the popular view that inside every funny man there is a deeply depressed, complicated and probably unpleasant person struggling to get out. The media fasten on to the peculiar personal habits of Kenneth Williams and Frankie Howerd, Milligan's depression, the alcoholism of Tony Hancock or Cook. In the process, the humour is overlooked.

Luckily, in all these cases, it survives on film and the likelihood is that audiences will be watching Cook and Moore long after Johnson's film is forgotten. As it happens, they will have a chance to do that on New Year's Day when The South Bank Show will televise extracts from Goodbye Again, a series originally made by Dud and Pete for ATV in 1968. The tapes were thought to have been lost along with the BBC's and have only recently been unearthed. Though not of the same quality as McGrath's Not Only But Also, they include some classic dialogues which are as funny as anything they ever did. So why watch actors pretending to be Dud and Pete when you can see the real thing?

· Not Only But Always is on Channel 4 at 9pm, 30 December

Peter's friends

Jonathan Miller Created the Beyond the Fringe revue with Cook, Alan Bennett and Dudley Moore while at Cambridge. They took the show to the Edinburgh Festival in 1960.

Alan Bennett Following Cook onstage, Bennett recalled he would 'be handed an audience so weak with laughter that I could do nothing with it'.

Dudley Moore Cook's longest-serving partner, Moore left him for Hollywood in 1975, damaging their friendship. He died in 2002.

Ian Hislop Appointed editor of Private Eye by Cook after Richard Ingrams's departure 18 years ago, angering much of the 'old guard' at the magazine.

Paul FootA founder member of Private Eye, Foot worked closely with Cook, who always encouraged his investigative journalism. He returned to the Eye under Hislop. He died this year.